# Presentation: 890083

## Thermal (Surface) Radiation from 

- <date/time>

-  Has been securely detected (e.g. by Chandra and XMM-Newton)
**           **Radio pulsars
-            Radio-quiet NSs (young CCOs in SNRs and “dim”  INSs=RICOs)
-              Magnetars
-               [Also: transiently accreting NSs]

**Thermal (Surface) Radiation from **
**Isolated Neutron Stars**

- M, R, EOS,
- cooling history (exotic processes),
- surface B and composition

- Yakovlev et al. 2002

## Neutron Star Surface and its Radiation

- <date/time>

**Neutron Star Surface and its Radiation**

- 0.   Overview of NS atmosphere physics
- Radiative transfer in magnetized NS atmospheres:
-       Effect of strong-field vacuum polarization
- 	  *Wynn Ho (moving to Hubble postdoc at Kavli Institute at Stanford)*
- Radiation from condensed NS surface
-         *Matt van Adelsberg*
*          **Phil Arras (now postdoc at KITP)*

**Dong Lai (Cornell)**

- Also collaborating with
-            *Alexander Potekhin (St Petersberg)*
*           **Gilles Chabrier (Lyon)*

**Notes:**
So I’d like to talk about two problems related to ...
This 1st problem cocnerns ... (This is relevant to most NSs, but perhaps not so for those transiently accreting ...)

## Neutron Star Atmospheres (Basics)

- <date/time>

**Neutron Star Atmospheres (Basics)**

**Strong gravity          NS atmosphere is highly compressed:**
-      *H* ~ 0.1 -- 10 cm
-        ~ 0.1 -- 103 g cm-3
-                  Highly nonideal gas (pressure ionization, etc.)

**       **

**Strong B field**
** **Anisotropic and birefringent medium (polarized radiation)
-  Property of matter is completely changed
-  Effect of vacuum polarization: important for superstrong  fields

**Current status of NS atmosphere modeling:**
-  B=0 atmospheres are well modeled (e.g.,Romani; Pavlov-Zavlin; Pons)
-  Magnetic atmosphere models: much remains to be done
-   (e.g., Shibanov-Pavlov-Zavlin, fully ionized ~1012G Hydrogen models)

**Notes:**
Let me begin by reminding you some basics about NS atmospheres:
First, there is a strong gravity, so the atmosphere is highly compressed...

Moreover, most NSs have strong B fields,
That means we have an anisotropic and birefringent medium, so we have to deal with polarized radiation.
Most importantly, in strong B fields the property of matter is completely different from the b=0 case,
And in the superstrong field regime (relevant to magnetars) we have to worry about the effect of vacuum polarization.
These are the issues we have to understand when we model NS atmospheres.
 Currently, 

## Matter in Strong B-Fields (Summary)

**Matter in Strong B-Fields (Summary)**

- References: Ruder et al. 1994;  Potekhin 1998; Mori & Hailey 2002;
-                    Lai 2001, RMP (and references therein)

**Notes:**
Here is a one-page summary of the property of matter in strong B.
When B>10^9G, the properties of atoms, molecules and condensed matter are completely different from the B=0 case.
So when we study surface layers/atmospheres of NSs,  these need to be properly taken into account. 
So far, we (meaning the community) are still in the early stages of incorpoarting these into the atmosphere models.
In fact, with Potekin and Chabrier, we have recently constructed the first ...

- <date/time>

- Ho, Lai, Potekhin & Chabrier (2003)

**“****First” Magnetic,  Partially Ionized H Atmosphere Models:**

- NS atmosphere is not a blackbody emitter: has hard tail
- 	(due to nongrey opacity)

**Notes:**
These are actually the first magnetic atm models that 
Includes partially ionzed H (that is the red curve). Previous work has assumed  full ionization (blue).
The B field here is ... and T_eff is 
You can see there are spectral features, but they are in the UV band (for this B), and therefore hard to detect.
But the real purpose of showing this plot is to remind you that ...

## Observations show: NS thermal spectra are often (but not always)featureless and close to blackbody

- <date/time>

- Juett et al 2002; also Patel et al 2003

- Burwitz et al 2003; see also Walter

- RX J1856-3754

- AXP 4U 0142+61

**Observations show: **NS thermal spectra are often (but not always)featureless and close to blackbody

- Proton cyclotron energy = 0.63 B14 keV
- Why not there?

**Notes:**
Observations, however, show that ...

## Why are observed spectra often featureless blackbody? 

- <date/time>

**Why are observed spectra often featureless blackbody?**

- Two pieces of physics:

-  Effect of vacuum polarization on radiative transfer in
-   NS atmospheres
-  Possible condensation of NS surface

**Notes:**
So the question is ...
So I’d like to tell you 2 pieces of physics that may provide an answer.
The 1st one concerns ...
The 2nd one ...
(I am not going to focus on specific sources, but rather will discuss the generenal physics effects)

## Vacuum Polarization in Strong B

- <date/time>

**Vacuum Polarization in Strong B**

- Virtual photon

- Virtual photon

- Important when B>BQ=4.41013G

**Notes:**
What is VP? 
(Even if you haven’t studied QED, you most likely have heard (read) that)
Simply speaking, vacuum is not really vacuum,
It is permeated by virtual photons and virtual pairs.
When you have a strong B field, these paris are polarized, and therefore the vacuum is birefringent.
And this will affect photon propagation.

## Summary: Vacuum Polarization Effect on Thermal                         Emission from Magnetic Neutron Stars:  

- For B>71013G, vacuum polarization affects spectrum significantly:
-       1. Soften hard tail, making the spectrum closer to blackbody
-       2. Suppress spectral lines

- Ref: Lai & Ho 2002,2003; Ho & Lai 2003a,b

**Notes:**
So how does vp affect ...
Let me first tell you the answer before expalining the physics.

## B=1014G Model

- <date/time>

**B=10****14****G Model**

*Blackbody*

*T=5.10**6**K*

*No vacuum*

*With vacuum*

**Notes:**
Here is an example: 

- <date/time>

**B=5********10****14****G Model**

*No vacuum*

*With vacuum*

- Proton cyclotron
-    =0.63B14keV

## Two example of AXP spectra

- <date/time>

- Juett et al. 2002; Patel et al 2003

- Tiengo et al.2002

***AXP 4U0142+61***

***AXP 1E1048-5937***

***Chandra (HETGS)***

***XMM-Newton***

***Blackbody T=0.4 keV***

***Power-law n=3***

***Blackbody T=0.6 keV***

***Power-law n=2.9***

**Notes:**
What does the observation say?
Here are two examples of AXP spectra. Despite deep searches, no spectral feature has been found.
We think this because vp is in action.

- <date/time>

**Vacuum polarization effect on radiative transfer:**
**How does it work?**

**Notes:**
So how does vp affect ...

## Photon Polarization Modes in a Magnetized Plasma 

**Photon Polarization Modes in a ****Magnetized Plasma**

**Notes:**
First, some basics about ...
A magentized plasma is anisotropic and birefringent.
When we consider a photon (or EM wave) propagating in a magnetized plasma, there are two polarization modes...

This distinction is important because ....

## Vacuum Polarization in Strong B

***-***

***+***

***e***

***e***

*photon*

*photon*

**Vacuum Polarization in Strong B**

**Notes:**
So how does vp affect radiative trasnfer?
(It has been known for a long time that in a magnetic field, even a vacuum has a nontrivial dielectric ...
This is a QED effect.)
As I mentioned, QED tells us even a vacuum has a nontrivial dielstric property
So for a magnetized plsama, the dielectric tensor has both plasma contribution and ...
VP also contributes ti the permeability tensor..
The magntiztude of the vacuum contributions is roughly of order ...; so it is rather small unless B is much greater thab B_Q.

However, thers is a dreamatic effect called vacuum resonance. 
This occurs when ...

## Property of photon modes

- Lai & Ho 2002

- res

- B=1014 G,  E=1 keV,  B=45o

## Mikheyev-Smirnov-Wolfenstein  (MSW)Neutrino Oscillation

**Mikheyev-Smirnov-Wolfenstein  (MSW)****Neutrino Oscillation**

**Notes:**
In the solar neutrino case ...

## Adiabatic Evolution of a Quantum State

- <date/time>

**Adiabatic Evolution of a Quantum State**

**Notes:**
The key concept (in both problems) is “adiabatic evolution” , which is illustrated by the pendulem  problem.

It is actually easier (more intuitive) to think about it in QM.

Suppose you have a pendulem and it is in a certain eigenstate. 
Suppose you very slowly increase the length of the pendulem,
Then it is still going to be in the same eigenstate (the wavefunction has the same shage, except it is stretched).

## Property of photon modes

**Lai & Ho 2002**

- res

- B=1014 G,  E=1 keV,  B=45o

**Notes:**
Here in the photon propagation problem,
Suppose we have a O-mode photon propagating outward from the high density region ...
If the density variation is sufficiently gentle, it is going to evolve adiabtically along the red curve (remains in the same eigenstate),
And as the photon crosses the resonance, it  is converted into a X-mode.

## An illustration of Mode conversion

**Notes:**
Here is what happened if you want to think about it in pictures.
Suppose at high denisty, you have a photon in X-mode, it is polarized this way.
Then as the photon travels to low denisty regime, crossing the vacuum resonance, the orientation of the polarization
Ellipse will be perpendicular to 

So that is what I mean by resonat mode conversion due to vacuum polarization.

##        Adiabatic Condition: 

**       ****Adiabatic Condition:**

**Notes:**
Of course (as mentioned), for the mode conversion to be effective, the adiabatic condition must be satisfied.
Namely the denisty gradient must be sufficiently gentle compared to the difference in the indices of refraction.
This translates to ...

## An illustration  of mode conversion effect 

**B>7********10****13****G regime:**

**Notes:**
So why does the mode conversion matter?

## B=1014G Model

- <date/time>

**B=10****14****G Model**

*Blackbody*

*T=5.10**6**K*

*No vacuum*

*With vacuum*

**Notes:**
Here is an example: 

- <date/time>

**B=5********10****14****G Model**

*No vacuum*

*With vacuum*

- Proton cyclotron
-    =0.63B14keV

## 	 o-mode  < res < x-mode

-     Vacuum resonance lies between
-      the two photospheres
- 	 o-mode  < res < x-mode
**For B<7********10****13****G:**
-      Vacuum resonance lies outside
-      both photospheres
- 	res  < o-mode < x-mode
-           Vacuum polarization effect
-           on  spectrum is negligible

**Notes:**
So that is for magnetar-like fields, where the vacuum resonance lies between ...

- <date/time>

**For B<7********10****13****G, vacuum polarization effect on spectrum is negligible**
** **

**B=4********10****13****G Model**

- Ho & Lai 2003b

**Notes:**
So that for magetar field. What about more ordinary field strength?
If B is less than ...

## Synthetic spectrum:

- <date/time>

**Synthetic spectrum:**

- Ho & Lai 2003b

## Neutron star RBS 1223 (=RX J1308+2127):                   Broad  absorption feature at ~ 0.2-0.3 keV

- <date/time>

**Neutron star RBS 1223 (=RX J1308+2127):**                   Broad  absorption feature at ~ 0.2-0.3 keV

**Haberl et al. 2003**

**Also, 0.4 keV features in RX J1605+3249 (van Kerkwijk et al;**
**	****	****	****	****	****see Kaplan’s talk)**

## Summary: Vacuum Polarization Effect on Thermal                         Emission from Magnetic Neutron Stars:  

- <date/time>

**Summary:**** ****Vacuum Polarization Effect on Thermal      ****                   Emission from Magnetic Neutron Stars:**** **

- For B>71013G, vacuum polarization affects spectrum significantly:
-       1. Soften hard tail, making the spectrum closer to blackbody
-       2. Suppress spectral lines

- For B<71013G, negligible effect on spectrum (spectral lines possible)

- Ref: Lai & Ho 2002,2003; Ho & Lai 2003a,b

**But dramatic effect on X-ray polarization**

**B=10****13****G Model**

**Plane of linear polarization at <1 keV is perpendicular to that at >3 keV.**

##        Adiabatic Condition: 

**       ****Adiabatic Condition:**

**Notes:**
Of course (as mentioned), for the mode conversion to be effective, the adiabatic condition must be satisfied.
Namely the denisty gradient must be sufficiently gentle compared to the difference in the indices of refraction.
This translates to ...

**B<7********10****13****G regime:**

**Notes:**

Here is a cartoon of NS atmosphere with ordinary field strength.  (The B field is on the plane of the screen)
I am showing the photospheres of the two photon modes and the vacuum resonance.
(Because the two photon modes have different opacities, we have two photospheres...

For such field strength, the vacuum resonance occurs outside the photospheres.
Then the following will happen:

So we have a prediction: name the low-E photon and high-E photons will have linear polarizations
That are ortogonal to each other.

## Condensation of Neutron Star Surface

- In strong B-field, the outmost layer of neutron star may be in a
- condensed state (liquid or solid),  with no/little gas above it

**For H  (He) surface:**  know enough about the condensed matter
-  phase diagram:
-          Condensation is possible at
-          B>1015G and T<106 K   (approximately)
- 				            Lai & Salpeter (1997), Lai 2001

- First suggested by Ruderman in 1970’s (based on rather crude calculation)

**For Fe surface:**  we are ignorant
-          Condensation might be possible even for ~1012G and T~106K

- What is the radiation spectrum from condensed NS surface?

## Emission from condensed Fe surface:

- <date/time>

**Emission from condensed Fe surface:**

- B=1012 ,1013G,   T=106K

- Van Adelsberg. Lai & Arras
-        2003 in prep

## Summary

-       1. Soften hard tail, making the spectrum closer to blackbody
-       2. Suppress spectral lines
-       Current AXP/SGR data “show” QED at work

- For B<71013G, negligible effect on spectrum (spectral lines possible, observed!),
-       but dramatically affect X-ray polarization  (unique signature of vacuum
-       polarization, measurable with future X-ray polarimeters)

**Summary**

**Vacuum polarization (QED effect) can affect radiative transfer in **
**magnetic neutron star atmospheres a dramatic ****(and beautiful)**** way:**

**Possibility of surface condensation remains open **

- Radiation from condensed surface is relatively featureless
- and quasi-blackbody

**More work needs to be done (neutral species, dense plasma ...)**

**Notes:**
Here the blue curve shows the photosphere densities of X-mode photons as a function of E when vacuum polariztion is ignored. You see that photon with energy near the proton cyclotron resonance escapes from low
Density region, and that is why you get absoprtion.

With vacuum polatriozation include, the X-mode photons will emerge from the vacuum resonance denisty.
SO you see the difference between the line center and the continuum is small.

## An illustration  of mode conversion effect 

**B>7********10****13****G regime:**

**Notes:**
In the magnetar field regime, we have a situation where the vacuum resonance lies between the two
Photospheres, so we would not expect such a strong E dependence.

## Why are observed spectra often featureless blackbody? 

**Why are observed spectra often featureless blackbody?**

- Two pieces of physics:

-  Effect of vacuum polarization on radiative transfer in NS atmospheres
-  Possible condensation of NS surface

**Observations show: **NS thermal spectra are often (but not always)
- featureless and close to blackbody

- Juett et al 2002; also Patel et al 2003

- Burwitz et al 2003; see also Walter

**Notes:**
So the question is ...
So I’d like to tell you 2 pieces of physics that may provide an answer.
The 1st one concerns ...
The 2nd one ...
(I am not going to focus on specific sources, but rather will discuss the generenal physics effects)